9(4x-4)(6x+9)=0

Solution for 9(4x-4)(6x+9)=0 equation:

Simplifying
9(4x + -4)(6x + 9) = 0

Reorder the terms:
9(-4 + 4x)(6x + 9) = 0

Reorder the terms:
9(-4 + 4x)(9 + 6x) = 0

Multiply (-4 + 4x) * (9 + 6x)
9(-4(9 + 6x) + 4x * (9 + 6x)) = 0
9((9 * -4 + 6x * -4) + 4x * (9 + 6x)) = 0
9((-36 + -24x) + 4x * (9 + 6x)) = 0
9(-36 + -24x + (9 * 4x + 6x * 4x)) = 0
9(-36 + -24x + (36x + 24x2)) = 0

Combine like terms: -24x + 36x = 12x
9(-36 + 12x + 24x2) = 0
(-36 * 9 + 12x * 9 + 24x2 * 9) = 0
(-324 + 108x + 216x2) = 0

Solving
-324 + 108x + 216x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '108'.
108(-3 + x + 2x2) = 0

Factor a trinomial.
108((-3 + -2x)(1 + -1x)) = 0

Ignore the factor 108.
Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.5, 1}